Graph Transformations and Asymptotes

The video tutorial explains how to match equations with graphs by analyzing exponential growth and decay functions. It covers the effects of parameters 'a', 'b', and 'k' on graph transformations, including vertical stretches, compressions, and reflections. Examples are provided to illustrate these concepts, and the process of verifying equations using graph points is demonstrated. The tutorial concludes with labeling graphs with the correct equations.

What is the basic form of the exponential functions discussed in the video?

• f(x) = a * b^x + k

• f(x) = a + b^x * k

• f(x) = a * x^b + k

• f(x) = a * b^k + x

What happens to the graph when b is greater than 1?

• The graph remains constant.

• The graph becomes a linear function.

• The graph shows exponential growth.

• The graph shows exponential decay.

How does a positive value of k affect the graph?

• Shifts the graph down k units.

• Shifts the graph up k units.

• Compresses the graph vertically.

• Reflects the graph across the x-axis.

What effect does a negative value of 'a' have on the graph?

• It stretches the graph vertically.

• It shifts the graph horizontally.

• It compresses the graph vertically.

• It reflects the graph across the x-axis.

What is indicated by a horizontal asymptote at y = -3?

• The graph is shifted up 3 units.

• The graph is shifted down 3 units.

• The graph is reflected horizontally.

• The graph is compressed vertically.

Which of the following indicates exponential decay with a vertical reflection?

• b > 1 and a > 0

• b < 1 and a < 0

• b > 1 and a < 0

• b < 1 and a > 0

What is the horizontal asymptote of the graph on the right?

• y = 0

• y = 1

• y = 3

• y = -3

Which equation corresponds to a graph with a horizontal asymptote at y = 3 and a vertical reflection?

• y = 2 * 2^x + 3

• y = -2 * 2^x + 3

• y = -2 * 2^x - 3

• y = 2 * 2^x - 3

What is the y-intercept of the graph on the left?

• (0, 5)

• (0, 3)

• (0, -5)

• (0, -3)

Which point verifies the equation y = -2 * (1/2)^x - 3 for the graph on the left?

• (-1, -5)

• (1, -7)

• (-1, -7)

• (1, -5)